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Ta có:
A=1.3.5+3.5.7+5.7.9+...................+2015.2017.2019
8A=1.3.5.8+3.5.7.8+5.7.9.8+.......................+2015.2017.2019.8
8A=1.3.5.(7+1)+3.5.7.(9-1)+5.7.9.(11-3)+......................+2015.2017+2019.(2021-2013)
8A=1.3.5.7+15+3.5.7.9-1.3.5.7+5.7.9.11-3.5.7.9+.........................+2015.2017.2019.2021-2013.2015.2017.2019
8A=15+2015.2017.2019.2021
A=(15+2015.2017.2019.2021)/8
t i c k cho mình nha mình suy nghĩ khá lâu đấy
1.3.5+3.5.7+5.7.9+...+97.99.101
=(101-2).(101-1).101.(101+1):4
=25497450
1.3.5.8 + 3.5.7.8 + 5.7.9.8 + … + 95.97.99.8
= 1.3.5(7 + 1) + 3.5.7(9 - 1) + 5.7.9(11 - 3) + … + 95.97.99(101 - 93)
= 1.3.5.7 + 15 + 3.5.7.9 - 1.3.5.7 + 5.7.9.11 - 3.5.7.9 + … + 95.97.99.101 - 93.95.97.99
= 15 + 95.97.99.101
=> \(A=\frac{15.95+97.99.101}{8}\)
A = 1/4.( 4/1.3.5 + 4/3.5.7+ ....+ 4/95.97.99)
= 1/4 .( 1/ 1.3 - 1/3.5 + 1/3.5 - 1/5.7 + .......+ 1/95.97 - 1/97.99)
= 1/4( 1/1.3 - 1/97.99)
= 1/4 . 9499/29397
\(\frac{36}{1\cdot3\cdot5}+\frac{36}{3\cdot5\cdot7}+\frac{36}{5\cdot7\cdot9}+...+\frac{36}{25\cdot27\cdot29}\)
\(=9\left[\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+...+\frac{4}{25\cdot27\cdot29}\right]\)
\(=9\left[\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5\cdot7}+...+\frac{1}{25\cdot27}-\frac{1}{27\cdot29}\right]\)
\(=9\left[\frac{1}{3}-\frac{1}{783}\right]=9\cdot\frac{260}{783}=\frac{260}{87}\)
Đặt \(A=\frac{36}{1.3.5}+\frac{36}{3.5.7}+\frac{36}{5.7.9}+...+\frac{36}{25.27.29}\)
\(\Rightarrow\frac{1}{9}A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+...+\frac{4}{25.27.29}\)
\(\Rightarrow\frac{1}{9}A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{25.27}-\frac{1}{27.29}\)
\(\Rightarrow\frac{1}{9}A=\frac{1}{1.3}-\frac{1}{27.29}\)
\(\Rightarrow\frac{1}{9}A=\frac{261}{783}-\frac{1}{783}\)
\(\Rightarrow\frac{1}{9}A=\frac{260}{783}\)
\(\Rightarrow A=\frac{260}{783}\div\frac{1}{9}\)
\(\Rightarrow A=\frac{2340}{783}=\frac{260}{87}\)
Đặt A = 1.3.5 + 3.5.7 + 5.7.9 + ...... + 47.49.51
8A = 1.3.5.8 + 3.5.7.8 + ...... + 47.49.51.8
= 1.3.5(7 + 1) + 3.5.7.(9 - 1) + ...... + 47.49.51(53 - 45)
= 1.3.5.7 + 1.3.5 + 3.5.7.9 - 1.3.5.7 + ......... + 47.49.51.53 - 47.47.49.51
= 1.3.5 + 47.49.51.53
=> A = \(\frac{1.3.5+47.49.51.53}{8}=778128\)
628414
chi tiết là ko biết bởi vì e mới học lớp 5